All posts by Daniel Scher

Daniel Scher, Ph.D., is a senior digital strategist at McGraw-Hill Education. He worked as a senior scientist at KCP Technologies, co-directing the NSF-funded Dynamic Number project.

Interactive Array Explorations

Arrays can be enormously helpful tools for helping young learners to visualize multiplication.  Early work with arrays also sets the stage for more advanced mathematics, like binomial multiplication. In this blog post, I present several interactive arrays built with Web Sketchpad as part of the Dynamic Number project. The interactive array model below (and … Continue Reading ››

Fifth Graders Investigate a Mathematical Code

How much tolerance do you have for puzzlement? When faced with a mathematical conundrum, do you embrace the challenge, or do you feel some trepidation at confronting the unknown? For many of us, an unfamiliar mathematical task is sure to raise our heart rate a beat or two. As teachers, it’s easy to translate these fears … Continue Reading ››

Deducing the “Mystery” Fraction

Estimation is an important mathematical skill, yet we rarely ask students to make estimates that relate to fractions. As part of the Dynamic Number project, we created a "mystery" fraction challenge  that presents a green point somewhere between 0 and 1 on the number line. The point's location can be represented as a fraction with … Continue Reading ››

Binomial Multiplication and Factoring Games

The four Web Sketchpad activities below from our Dynamic Number project  provide a sequenced collection of challenges and games that develop an area model approach to binomial multiplication and factoring. You can click any of the images to open the interactive websketches on a separate page.

Dynamic Algebra Tiles, Part One

In the first websketch, students … Continue Reading ››

Algebra Cross Number Puzzles

In my previous post, I wrote about cross number puzzles—puzzles that mix arithmetic and logic to introduce students to place value, commutativity, and the addition and subtraction algorithms. Now, I'd like to present a variant of cross number puzzles that adds some algebra to the mix. Below (and here on its own page) are … Continue Reading ››

Cross Number Puzzles

We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››

Exploring Multiples on a Dynamic Number Grid

What would it take to build a better number grid for young learners? A typical number grid contains 10 columns with the numbers progressing from 1-10, 11-20, 21-30 and so on, from row to row. We decided to upend this tradition and make a dynamic number grid with Web Sketchpad that allows students to choose … Continue Reading ››